How do you prove that EF || AB ?

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How do you prove that EF || AB ?

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Answer 1 · 2018-04-29T10:57:08

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Explanation:

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In $△ A D M,$ $triangle ADM,$
$∠ A + ∠ M = ∠ D = α + β$ $angle A + angle M = angle D = alpha + beta$

Given $∠ A = α :$ $angle A = alpha :$
$α + ∠ M = α + β$ $alpha + angle M = alpha + beta$
$\Rightarrow ∠ M = β$ $=> angle M = beta$

$E M$ $EM$ is $transversal$ $"transversal"$ crosses $A B and E F, ∠ M = ∠ E = β$ $AB and EF, angle M = angle E = beta$
$\Rightarrow A B || E F$ $=> AB " || " EF$

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How do you prove that EF || AB ?

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